FIRST IMPRESSIONS:
I've been hyped up to watch this anime and I've got to say it starts off pretty strong - not forcing expository dialogue or monologue, not forcing long-winded character introductions or even an overdrawn establishment of motive. It's very easy to understand what is to come from these characters - Simon and Kamina and I think they will be the driving forces of the series for sure. I like how it shoves you right into the action for you to figure it out, like a shounen should. Like, I'm getting vibes of a true shounen / mecha anime, since Kamina keeps going on about manly spirit and I think the characters brute forcing their way through things will be a sight to behold (if that's what the series ends up doing).

FIRST ARC:
Wow, a series like this has never moved me so - from the inspirational quotes to the wonderful characterisation I think this anime (even at the halfway mark) manages to mean and be a lot more than any other show out there. The establishment of Kamina and Simon's relationship at the start were integral to accelerating the plot to the insane degree that it went, making the climax that much more satisfying. Even though this anime was made many years ago, it breaks the conventional standards of modern anime, from establishing relationships, to killing off a main character and it does so in a way that is not trying too hard to break those conventions. Yoko and Kamina's final kiss packed a lot of emotion for both Yoko and Kamina themselves as well as Simon making this battle that they were about to have to claim the Dai-Gurren. In killing Kamina that episode broke most of my expectations for the show, like I was even expecting Kamina to come back in the arc but they were committed. Not only were they committed to Kamina's death, but they used that to push the main character through his personal conflicts and as such develop him as a character - resulting in both Simon's character to be strengthened and become more of a realised character than he was in the first couple of episodes, as well as Kamina's legacy to be honoured. All of the main characters growing makes me fear for what might happen in the future, as this arc is only half of the actual series itself, which is a good thing for the show because it is evidence of how it has made me care about these characters.
Of course, there are some issues that I had with the series in that some of the characters are just for 'gag' purposes, although I haven't fully seen what they will do with them in the following arc but some characters are just there for a joke every now and then, but I guess that is okay. Just a bit of a minor grip is all. Some minor character introductions were a bit awkward as well, although they managed to eventually fit into the cast quite well so I can't put that blame on the series. Even the 'arc nemesis', Viral, was pretty cool in my opinion. Becoming enemies with Kamina ever since the first encounter with their battles going further and further until Viral realises that Kamina is dead. Just the obsession with the villain to rematch Gurren-Lagann even at the cost of the other bosses' fight with Gurren-Lagann makes the villain seem that much more realised and I really appreciate that.

My largest complaint so far was probably episode four, with the drastically different art and directing style kind of disrupting the already slow flow of the first few episodes. This makes the series pretty slow to start getting into, but once it starts picking up. Oh man. It gets really good.
The build up for the battle with the Spiral King was insane, with (in typical shounen style) the four big bosses coming at the cast and seeing how they deal with it was just exhilarating. This hype combined with Simon's reformed character after his mini Kamina arc has been resolved makes for a wonderful shounen experience backed with many feels and emotion. Additionally (of course) this is definitely helped with Trigger's expressive and impactful art style that really packs a punch when the series is going crazy with its action scenes and, combined with the music, makes the hype that much better. Going even further the OP adds to this hype by adding in small details like extra characters or putting in relevant information to suit what the characters are going through - though this is (of course) only happening during major changes I still appreciate the touch from the first OP to like the 7th OP - cool touch Gainax :^).
I would describe this arc as a snowball, slowly starting off but going incredibly fast and hard when it has that acceleration going on. I think this hype is going to carry itself into the next arc and be even greater. I think this anime is most likely going to make it into my top 10 favourite series, but I guess I'll just have to wait and see for the next arc and conclusion to see.

SECOND ARC & FINAL COMMENTS:
Wow. What more can I say than, wow. What a ride this anime was, not only having one of the best build ups to a climax that I have ever experienced but also having one of the best pay offs that I have ever seen. The show ends on such a wonderful note and wraps up pretty much everything that it could have, the characters and the overall plot. A very satisfying and wholesome experience I would say, which is very rare to see even in some modern anime these days.

The second arc does start off slow, since it basically has to establish everything from the bottom up due to it being a new society and whatever. I appreciated the time that they took in allowing the audience to understand the values of the people and the main characters that have changed over the years since they defeated the Helix King. Overall the pacing was pretty much perfect and allowed efficient enough breathing space for both the main characters to finish all of their arcs as well as for the villains to build up enough of a threat that would make you question how the hell Simon's going to make it. Which is exactly what a shounen anime should be doing.

This starting section, being quite slow, allowed for the emotions to brew as the audience was positioned to dislike Rossiu and feel hopeless for Simon in his plight to save the people and be like he was in the previous arc. Painting the vastly different picture of these characters makes the experience feel different from the first arc whilst keeping the spirit of the series as a whole, and this was the first step in allowing for this series to built its own hype so well. The various sacrifices by the minor characters had their own impacts and contributed to that major build up propelling the final battle to be so great. Not only showing the threat of the Anti-Spirals but also the determination of the Dai-Gurren squad to defeat the overarching enemy of the entire series. I think that the lead up to defeating the Anti-Spiral coming from the smaller-scale Helix King allowed the series to cohesively elaborate on the plot as a whole.
Speaking of the villains, it was a nice sight to see both the Helix King and Viral come back into the cast first as hostile but eventually it felt natural that they were important to the plot. Bringing them back was not just an excuse to please the fans of those respective characters, but it was important in the overall battle and sense of wholesomeness that came with that final battle - with Viral getting some kind of closure in piloting Gurren and with the Helix King being able to face his previous enemy and close things up with his 'daughter'. Adding to this wholesomeness was the little alternate realities thing where Kamina showed up and allowed all of the main cast to transform into Tengen Toppa Gurren Lagann. That sense of closure that Kamina gave Simon made the series go full circle and helped to close everything off for me.
The art of the series was great, showing the highest amount of impact that it could when it needed to with the thick outlines and rough 'action lines' allowing for everything to feel very heavy. The final battle showed the highest amount of artistic effort and I really appreciated how good it was considering how many fights there were in the arc. Studio Gainax did a good job in maintaining their budget I guess. On the note of art, the music that went along with it propelled the hype further and made the experience feel very shounen in its nature.
The major antagonist in the series, I felt, would have benefited from a bit more breathing space in terms of establishing the foundation of his principles and where he stands in terms of the whole situation. I know this is basically clear in that he just wants to exterminate all spiral beings but I feel as though that could have been expanded in a way that would have made the audience question their morals. I think that the best antagonist to a story is both one you can relate to as well as one that may have an equal moral standing to the characters, i.e. their reason for wanting to defeat the protagonist is just as good as why the protagonist wants to defeat the antagonist. This balance is the most important factor in allowing for there to be a sense of belief in the villain and the plot itself. However, the show does an alright job for itself in establishing him anyways, and I think that with Viral and the Helix King stepping back in it kind of reconciles those little criticisms - since their intentions follow the aforementioned principles to a good villain (imo).

Enough complaining though. This anime moved me in many ways, made me emotional and excited and I really understand the love behind this series. Even though it was slow to start, I think that the build up was worth the insanely satisfying pay off and I would easily put this as one of my favourite series. A very very strong 9.